Kinetic energy from the cubic sum rule of the dynamic structure factor

Abstract The third frequency moment sum rule of the dynamic structure factor is explored for the first time as an alternative estimator of the kinetic energy K of quantum many-body systems. As a practical example, the uniform electron gas at warm dense matter conditions is considered. First, K is extracted from quasi-exact ab initio path integral Monte Carlo results for the imaginary-time density-density correlation function and the expected excellent self-consistency with the thermodynamic differentiation route is confirmed. Second, K is extracted from approximate dielectric formalism results for and it is observed that common semi-classical approximations lead to a wave-number–dependent K with an incorrect short-wavelength limit. Our results are expected to be of broad interest for a great variety of applications, including time-dependent density functional theory, dielectric formalism schemes and warm dense matter models, as well as for the design of dedicated x-ray Thomson scattering experiments with the potential to provide model-free access to the full electronic equation of state.